Non linear effects in optical fibers
- 1. Non Linear Effects in Optical Fibers MEC
- 2. Non Linear Effects • Stimulated Scattering - Stimulated Brillouin Scattering - Stimulated Raman Scattering • Optical Kerr Effects - Self Phase Modulation - Cross Phase Modulation - Four Wave Mixing
- 3. Nonlinear effects • Due to interactions between light waves and the material transmitting them. • Nonlinear effects are weak at low powers, much stronger at high optical intensities. • Can result when the power is increased, or when it is concentrated in a small area such as the core of a single-mode optical fiber. • Accumulate as light passes through many kilometers of single-mode fiber.
- 4. Nonlinear Effects • Refractive index = f (Frequency, Light intensity). • Optical power can be increased to overcome losses. • Non linear effects significant at high optical • power densities in long single-mode fibers. • Optical system performance degrades - reduction in power or gain in power at different wavelengths, frequency shift, adjacent channel crosstalk, wavelength conversion. • Non linear effects - stimulated scattering, optical Kerr effects, can be useful (amplification).
- 6. Stimulated Brillouin Scattering • Modulation of light through thermal molecular vibrations within the fiber. • Scattered light appears as upper and lower sidebands. • Incident photon after scattering produces a phonon of acoustic frequency as well as a scattered photon. • Frequency of the sound wave varies with acoustic wavelength. • Produces optical frequency shift - varies with scattering angle.
- 7. Phonon • Quantum of an elastic wave in a crystal lattice. • When the elastic wave has a frequency f, the quantized unit of the phonon has energy = hf joules, h - Planck’s constant.
- 8. Stimulated Brillouin Scattering • Backward Process - maximum in backward direction, reducing to zero in forward direction. • Significant above threshold power density. • Threshold power d - fiber core diameter, λ - operating wavelength, ν -source bandwidth GHz, αdB – fiber attenuation dB/km.
- 9. Stimulated Brillouin Scattering • Brillouin shift from photon-acoustic photon interaction. • Brillouin threshold power gB - Brillouin gain coefficient, vp - signal line width, vB - Brillouin gain bandwidth, Aeff - effective core area . • Non linear effect contributes to signal impairment, additional power needed at the receiver to maintain the same BER.
- 10. Reduction in Power Penalty • Power level per WDM channel kept much below SBS threshold, spacing between amplifier stages reduced in long-haul systems. • Line width increased by direct modulation of source, may result in dispersion but can be reduced by dispersion management.
- 11. Stimulated Raman Scattering • Interaction between the incident optical signal (photon) and molecular vibrations. • Some part of the energy of the incident photon absorbed by the molecule. • Scattering of the photon, a high-frequency optical phonon generated. • Frequency and energy of the incident photon reduces, modified photon is called Stokes photon.
- 12. Stimulated Raman Scattering • Incident optical signal is called a pump wave. • Reduction in frequency is equal to the molecular vibration frequency, called Stokes frequency • Can occur in both the forward and backward directions. • Optical power threshold of up to three orders of magnitude higher than the Brillouin threshold. • Raman Threshold - input power level that can induce the scattering effect so that half of the power (3-dB power reduction) is lost at the output of an optical fiber of length L.
- 13. Stimulated Raman Scattering • Threshold optical power for SRS d, λ and αdB as specified earlier. • Raman threshold power for a single-channel optical system • α - attenuation coefficient, Aeff - effective core area, gR - Raman Gain Coefficient.
- 14. Reduction in SRS power penalty • Reducing channel spacing. • Channel power level below threshold level - Distance between amplifiers to be reduced. • Channel dispersion reduces SRS penalty.
- 15. Raman vs Brillouin Scattering • SBS and SRS not usually observed in multimode fibers - their relatively large core diameters make the threshold optical power levels extremely high. • Brillouin threshold occurs at an optical power level of around 80 mW, Raman threshold apprx. 17 times larger. • SBS does not produce adjacent channel crosstalk, SRS does.
- 16. Raman vs Brillouin Scattering • Brillouin shift from the photon-acoustic photon interaction, Raman shift due to photon-optical photon interaction. • SBS in backward direction, SRS in both forward and backward directions. • Brillouin scattering due to Bragg-type scattering from propagating acoustic waves, large number of molecules involved, Raman scattering due to individual molecular motion.
- 17. Raman vs Brillouin Scattering • SBS Stokes shift smaller (0.09 nm shift in 1550 nm), SRS Stokes shift (100 nm shift in 1550 nm). • Brillouin gain bandwidth extremely narrow than Raman gain bandwidth. • Threshold power level for SBS quite low compared to SRS.
- 18. Electro-optic Effects • Electro-optic effects - changes in refractive index of a material due to external electric field. • The field modulates the optical properties of the device. • First and second-order effects - refractive index a function of the applied electric field.
- 19. Electro-optic Effects • n’ = n(E) a1 – linear electro-optic coefficient, a2 – second order electro- optic coefficient. • Change in n due to linear effect is called Pockel’s Effect, ∆n = a1E. • Change in n due to the second-order term is called Kerr effect. ∆n = a2E2 = (λK)E2 K - Kerr Coefficient in m/V2, dependent on wavelength λ, Typical value of K = 3 x 10-15 m/V2 for glass. • All materials exhibit the Kerr effect. Only non-centrosymmetric materials exhibit the Pockels effect.
- 20. Kerr Effect • Kerr effect or Quadratic electro-optic effect - change in the refractive index of a material in response to an electric field. • Electric field is due to the light itself. • Proportional to the local irradiance of the light. • Four Wave Mixing, Self Phase Modulation, Cross Phase Modulation.
- 21. Four Wave Mixing • Four-wave mixing (FWM) or four-photon mixing. • Three optical frequencies, f1,f2 and f3 closely spaced in wavelength interacts, a fourth optical wave frequency ffwm = f1 + f2 - f3 is generated.
- 22. Four Wave Mixing • FWM component EFWM, at the output of fiber segment L, generated by 3 components E1, E2, E3 with angular frequency ω, refractive index n, non-linear refractive index χ and loss α F(α, L, ) is a function of fiber loss, fiber length, and propagation variation (phase mismatch) related to channel spacing and dispersion.
- 23. Four Wave Mixing • Output power of the ffwm and the efficiency of four-wave mixing depend on 1. Refractive index. 2. Fiber length. 3. Chromatic dispersion of the fiber. 4. Channel Spacing 5. Power densities of the contributing frequencies f1,f2 & f3 6. Higher order polarization properties of the material.
- 24. Four Wave Mixing • Independent of bit rate. • Number of FWM generated signal • N signals are involved in the FWM process. • FWM efficiency depends material dispersion, channel separation, fiber length, optical power level of each contributing channel.
- 25. Reducing FWM • Cannot be entirely eliminated. • To reduce FWM : 1. Uneven spacing between channels. 2. Increasing channel spacing. 3. Power to be launched into the fiber reduced. 4. Near-zero net chromatic dispersion maintained using segments of fibres with opposing non-zero dispersion characteristics after long spans of standard fiber cable.
- 26. Self Phase Modulation • Optical pulse exhibits a phase shift induced by refractive index, refractive index varies with intensity of optical signal. • Most intense regions of the pulse are slowed down, the most exhibit the greatest phase shift. • Phase shift changes the distances between the peaks of an oscillating function and oscillation frequency along the horizontal axis.
- 27. Self Phase Modulation • Phase shift equivalent to stretching out or squishing part of an oscillating function along its horizontal axis. • Wave is chirped, ordered variation in frequency.
- 28. Self Phase Modulation • Chirped pulse has the same envelope as the unchirped pulse, broadens the pulse in frequency domain, not the time domain.
- 29. Self Phase Modulation • Cause errors at the receiving end, severe in WDM systems. • For a propagation distance of L, the phase of signal Leff is the effective transmission distance.
- 30. Cross Phase Modulation • Due to the non-linear effect of refractive index on the optical intensity. • Can result in cross talk among WDM channels. • Non-linear phase shift on the jth channel, Im(τ) - optical intensity of the mth channel.
- 31. Cross Phase Modulation • In continuous-wave signals, CPM dominate over SPM. • Strongest when pulses completely overlap one another. • Low probability of channels simultaneously transmitting bit 1 reduces the effect of CPM on average. • Pulses at different wavelengths travel at different group velocities, cause pulses to walk off from one another, reduce the effect of CPM.
- 33. Cross Phase Modulation in WDM Systems • More the dispersion discrepancy among channels, more rapidly pulses walk off from one another. • Effect of CPM inversely proportional to dispersion discrepancies among channels in WDM systems. • Minimize the impairment caused by CPM, the channel separation and /or local dispersion to be properly chosen.
- 34. Thank You